Test Hypotheses Regarding Matched-Pairs Data
-A Football Coach Claims That $\alpha$

Test Hypotheses Regarding Matched-Pairs Data
-A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength. Use $\alpha$ $= 0.05$ . Assume that the distribution is normally distributed.
$\begin{array}{l|ccccccccc}\text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Before } & 215 & 240 & 188 & 212 & 275 & 260 & 225 & 200 & 185 \\\hline \text { After } & 225 & 245 & 188 & 210 & 282 & 275 & 230 & 195 & 190\end{array}$